Tropical Storm Harvey lashed central Texas with torrential rains on Sunday, unleashing "catastrophic" floods after the megastorm -- the most powerful to hit the United States since 2005 -- left a deadly trail of devastation along the Gulf Coast.

The storm has caused at least two deaths since making landfall late Friday as a Category Four hurricane, pummeling the town of Rockport outside Corpus Christi with sustained winds of 130 miles (215 kilometers) per hour, the National Hurricane Center (NHC) said.

One person was killed when their house caught fire in the Rockport area, local officials said.

And in Houston, a woman drowned when she left her car which had stalled in high water, local media reported citing police.

"Cannot emphasize enough how much flooding there is on roadways you are endangering yourself and our first responders by being out," Houston Police Chief Art Acevedo wrote on Twitter.

Harvey slowly weakened as it advanced, ripping off roofs, flipping mobile homes, and leaving hundreds of thousands of people in the dark on the Gulf Coast, home to some of the country's most important oil refineries.

The National Weather Service issued more than a dozen tornado warnings overnight for southeast Texas, including several in the Houston area.

Forecasts show Harvey hovering over the shore for the next days, dumping dangerous amounts of rain.

In Houston, a city of 2.3 million, the city streets turned into fast moving rivers with officials warning residents to stay home.

Hobby International, one of the city's two airports, announced that all flights were canceled "due to standing water on runways," while George Bush International was operating at limited capacity.

"Catastrophic and life-threatening flash flood ongoing!" the NWS said on Twitter. "This is an EXTREMELY DANGEROUS situation! Do not travel unless told to."

"CATASTROPHIC LIFE THREATENING FLOODING ONGOING ACROSS SE TEXAS," it later emphasized.

Houston officials said that their 911 phone system was overwhelmed with emergency calls, mostly from stranded motorists.

The governor visited a shelter for coastal evacuees in the state capital Austin and handed out food, describing the damage to homes and property as "sheer tragedy".

"Some of them had their homes mowed down. Some of them will not have a place to return to... It is our job to make sure they will be taken care of," he said.

The Federal Emergency Management Agency said there should be no illusions about the long-term impact.

"This is going to be an unprecedented long and frustrating event for the state of Texas," FEMA director Brock Long told MSNBC.

"The recovery from this disaster is going to be years."

Emergency services were struggling to make headway as the rains continued to pour down, although the Coast Guard managed to airlift at least 20 people and a dog to safety.

President Donald Trump, aware of the damage to George W. Bush presidency's for his tardy response to Hurricane Katrina, said he was closely monitoring relief efforts from Camp David in Maryland.

"We are leaving nothing to chance. City, State and Federal Govs. working great together!" he tweeted after a teleconference meeting with his cabinet to discuss the emergency operations.

He will visit Texas next week.

In Rockport, a local school and airport were among the places to suffer major damage while homes were also burnt to the ground as power cables caught fire. There were similar scenes in Houston and Corpus Christi.

"I've never seen anything like this. We do have strong winds -- we're right next to the bay -- but nothing like last night," Corpus Christi store owner Brandon Gonzalez told AFP.

Brian McNoldy, a hurricane expert at the University of Miami, said a strong ridge of high pressure was preventing the storm from dispersing.

"There's no sign of it really moving in a foreseeable future," he told AFP.

Coastal Texas is a fast-growing area, with some 1.5 million people moving into the region since 1999. It is also home to a large number of oil refineries and a number of major ports.

US authorities said about 22 percent of crude production in the Gulf of Mexico, accounting for more than 375,000 barrels a day, was shut down as of Friday.

"We recognize that the ports in this region are critical and vital to the nation's economy," said Captain Kevin Oditt, incident commander for the Coast Guard's Houston-Galveston post.

"We are preparing to open ports once the storm has passed or weather conditions permit."

In Victoria, a town just north of Rockport, residents were shocked by the storm's intensity.

"We didn't know it was going to be a Category Four storm so we thought we'll just ride it out," local resident Robby Villa told AFP.

"If I knew it was going to be what it came to be, I might have left sooner," he said.

Several locals, including Leslie Warner, worried about flooding.

"You know after the storm is done, from Austin and San Antonio, all that water is gonna come down here," she told AFP.

Harvey is the most powerful hurricane to hit the mainland since Wilma struck Florida 12 years ago.

2005 was a huge year for hurricanes -- before Wilma, Hurricane Katrina pummeled New Orleans, leaving more than 1,800 dead.